Out of a deck of 52, what is the probability you draw 4 cards and all four cards are DIAMOND cards? (You can see a deck of cards here.) a
.0026
b
.00000015
c
.077
d
.25

This decimal value is the approximation of the fraction 11/4165

Explanation:

There are 13 diamonds out of 52 total.

The probability of getting a diamond card is 13/52.

After selecting that diamond card and not putting it back, we have 13-1 = 12 diamonds left out of 52-1 = 51 left. The probability of getting another diamond is 12/51.

Then the probability of getting a third diamond is 11/50, and finally 10/49 represents the probability of getting a fourth diamond. Each time we need a new probability, we just subtract 1 from the numerator and denominator.

The numerators are: 13, 12, 11, 10

The denominators are: 52, 51, 50, 49

We'll multiply the four fractions to get our final answer

(13/52)*(12/51)*(11/50)*(10/49) = 0.00264105642257

This rounds to 0.0026 which is roughly a 0.26% chance

The answer as an exact fraction is 11/4165

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.